Algebraic classification of the gravitational field in Weyl-Cartan space-times
arXiv:2305.05501 · doi:10.1103/PhysRevD.108.044037
Abstract
We present a complete algebraic classification for the curvature tensor in Weyl-Cartan geometry, by applying methods of eigenvalues and principal null directions on its irreducible decomposition under the group of global Lorentz transformations, thus providing a full invariant characterisation of all the possible algebraic types of the torsion and nonmetricity field strength tensors in Weyl-Cartan space-times. As an application, we show that in the framework of Metric-Affine Gravity the field strength tensors of a dynamical torsion field cannot be doubly aligned with the principal null directions of the Riemannian Weyl tensor in scalar-flat, slowly rotating, stationary and axisymmetric space-times.
22 pages, minor changes, references added. It matches the version published in PRD Mathematica file as supplemental material available at https://community.wolfram.com/groups/-/m/t/2996064
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Cited by in corpus (4)
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- A unified-description of curvature, torsion, and non-metricity of the metric-affine geometry with the Möbius representation
- Algebraic classification of the gravitational field in general metric-affine geometries
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